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There exist two flavors of Proxy Data Adapter: NetworkedDataProvider and RobustNetworkedDataProvider.
In your case you are using the first one that explicitly provides not to start listening on the server TCP port until both the request_reply_port and notify_port (7001, 7002) are connected.

You can switch to RobustNetworkedDataProvider that allows the server to start even before the Remote Adapter has connected.

Code:

<adapter_class>ROBUST_PROXY_FOR_REMOTE_ADAPTER</adapter_class>

Furthermore, the RobustNetworkedDataProvider contains some recovery capabilities and avoid to terminate the Lightstreamer Server process. Full details on the recovery behavior are available as inline comments within the example adapters.xml file available in the “Lightstreamer/DOCS-SDKs/adapter_remoting_infrastructure/doc/adapter_robust_conf_template” folder.

You should consider that the Moderato Edition does not allow clustering. So, since you do not need more that one server, the Moderato edition handles the load exactly as "Allegro/Presto/Vivace" editions could do.
But you have to consider if your application needs additional features that are not included in the Moderato, such as an higher Items update frequency, additional client libraries other than JavaScript, direct email support, etc ... .
For a complete list of features available in the various editions please refer here.